Energy landscapes for machine learning.

Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. In particular, we can define quantities analogous to molecular structure, thermodynamics, and kinetics, and relate these emergent properties to the structure of the underlying landscape. This Perspective aims to describe these analogies with examples from recent applications, and suggest avenues for new interdisciplinary research.

Energy landscapes for a machine learning application to series data.

Methods developed to explore and characterise potential energy landscapes are applied to the corresponding landscapes obtained from optimisation of a cost function in machine learning. We consider neural network predictions for the outcome of local geometry optimisation in a triatomic cluster, where four distinct local minima exist. The accuracy of the predictions is compared for fits using data from single and multiple points in the series of atomic configurations resulting from local geometry optimisation and for alternative neural networks. The machine learning solution landscapes are visualised using disconnectivity graphs, and signatures in the effective heat capacity are analysed in terms of distributions of local minima and their properties.

Communication: Analysing kinetic transition networks for rare events.

The graph transformation approach is a recently proposed method for computing mean first passage times, rates, and committor probabilities for kinetic transition networks. Here we compare the performance to existing linear algebra methods, focusing on large, sparse networks. We show that graph transformation provides a much more robust framework, succeeding when numerical precision issues cause the other methods to fail completely. These are precisely the situations that correspond to rare event dynamics for which the graph transformation was introduced.

What is known about the role of clinical ethics services in cancer care? A systematic/narrative literature review.

The use of clinical ethics services (CES) has been increasing over time, but little is known about the role of CES in cancer care. Cancer diagnosis and treatment are emotionally charged and life-changing experiences, raising existential and ethical questions about the quality and meaning of, living and dying. This narrative review seeks to consolidate the available information regarding how CES are accessed and used in cancer care. The review attempts to answer the question, 'What is known about the role of CES in cancer care?' Papers included in this review were identified through searching PubMed and MEDLINE Ovid; a variety of keywords were used to ensure the capture of all relevant literature. 387 papers were identified using the search strategy, 13 papers were included in the final synthesis following the application of the inclusion and exclusion criteria. Citation searching was conducted. 11 of 13 papers were conducted in the USA, 1 in Germany and 1 in South Korea. A variety of study designs were incorporated into this review. Five key roles of CES in cancer care were identified; conflict resolution/mediation, delivery of ethics education to clinical staff, advising on specific aspects of care, guideline development/resource allocation and emotional support of clinicians. This narrative review outlines how CES can assist clinicians to reflect on, better understand and address, the complex ethical dimensions of their practice. The identified literature demonstrates that early involvement of CES may reduce conflict. More research is needed gathering information from CES directly.

The ultimate fate of supercooled liquids.

In recent years it has become widely accepted that a dynamical length scale ξ(α) plays an important role in supercooled liquids near the glass transition. We examine the implications of the interplay between the growing ξ(α) and the size of the crystal nucleus, ξ(M), which shrinks on cooling. We argue that at low temperatures where ξ(α) > ξ(M) a new crystallization mechanism emerges, enabling rapid development of a large scale web of sparsely connected crystallinity. Though we predict this web percolates the system at too low a temperature to be easily seen in the laboratory, there are noticeable residual effects near the glass transition that can account for several previously observed unexplained phenomena of deeply supercooled liquids including Fischer clusters and anomalous crystal growth near T(g).

On the surface of glasses.

Dynamics near the surface of glasses is generally much faster than in the bulk. Neglecting static perturbations of structure at the surface, we use random first order transition (RFOT) theory to show the free energy barrier for activated motion near a free surface should be half that of the bulk at the same temperature. The increased mobility allows the surface layers to descend much further on the energy landscape than the bulk ordinarily does. The simplified RFOT calculation, however, predicts a limiting value for the configurational entropy a vapor deposited glass may reach as a function of deposition rate. We sketch how mode coupling effects extend the excess free surface mobility into the bulk so that the glass transition temperature is measurably perturbed at depths greater than the naive length scale of dynamic cooperativity.

Constructing explicit magnetic analogies for the dynamics of glass forming liquids.

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations, we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on the liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy.

Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings.

We present a numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. [Phys. Rev. Lett. 106, 245502 (2011)10.1103/PhysRevLett.106.245502] and Asenjo et al. [Phys. Rev. Lett. 112, 098002 (2014)10.1103/PhysRevLett.112.098002] and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology, and machine learning that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom.

Structural analysis of high-dimensional basins of attraction.

We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties. The histogram method also allows us to directly obtain an estimate of the interior radial probability density profile, thus yielding useful insight into the structural properties of such a high-dimensional body. We illustrate the method by analyzing the effect of structural disorder on the basins of attraction of mechanically stable packings of soft repulsive spheres.

Thermodynamic-kinetic correlations in supercooled liquids: a critical survey of experimental data and predictions of the random first-order transition theory of glasses.

Thermodynamics and kinetics are thought to be linked in glass transitions. The quantitative predictions of alpha-relaxation activation barriers provided by the theory of glasses based on random first-order transitions are compared with the experimental results for 44 substances. The agreement found between the predicted activation energies near T(g) and experiment is excellent. These predictions depend on the configurational heat capacity change on vitrification and the entropy of melting the crystal which are experimental inputs.

Benchmarks for Characterization of Minima, Transition States, and Pathways in Atomic, Molecular, and Condensed Matter Systems.

A set of benchmark systems is defined to compare different computational approaches for characterizing local minima, transition states, and pathways in atomic, molecular, and condensed matter systems. Comparisons between several commonly used methods are presented. The strengths and weaknesses are discussed, as well as implementation details that are important for achieving good performance. All of the benchmarks and methods are provided in an online database to make the implementation details available and the results reproducible. While this paper provides a snapshot of the benchmark results, the online framework is structured to be dynamic and incorporate new methods and codes as they are developed.

Visualizing basins of attraction for different minimization algorithms.

We report a study of the basins of attraction for potential energy minima defined by different minimization algorithms for an atomic system. We find that whereas some minimization algorithms produce compact basins, others produce basins with complex boundaries or basins consisting of disconnected parts. Such basins deviate from the "correct" basin of attraction defined by steepest-descent pathways, and the differences can be controlled to some extent by adjustment of the maximum step size. The choice of the most convenient minimization algorithm depends on the problem in hand. We show that while L-BFGS is the fastest minimizer, the FIRE algorithm is also quite fast and can lead to less fragmented basins of attraction.